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3 years ago

(-2,1); perpendicular to y= - 2/5x -4 Help explain step by step?

Mathematics

1 answer:

Fittoniya [83]3 years ago

8 0

Answer:

y = (5/2)x + 6

Step-by-step explanation:

The given line has a slope (coefficient of x) of -2/5. The perpendicular line will have a slope that is the negative reciprocal of this:

-1/(-2/5) = 5/2

Since you are given a point you want the line to go through, the point-slope form of the equation of the line is useful. That form for slope m and point (h, k) is ...

y = m(x -h) +k

For your slope m=5/2 and point (h, k) = (-2, 1), the equation of the line is ...

y = 5/2(x +2) +1

y = 5/2x +6 . . . . . eliminate parentheses

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In the illustration below, the three cube-shaped tanks are identical. The spheres in any given tank

fredd [130]

Answer:

1) Volume occupied by the spheres are equal therefore the three tanks contains the same volume of water

2) $Amount \ of \, water \ remaining \ in \, the \ tank \ is \ \frac{x^3(6-\pi) }{6}$

Step-by-step explanation:

1) Here we have;

First tank A

Volume of tank = x³

The volume of the sphere = $\frac{4}{3} \pi r^3$

However, the diameter of the sphere = x therefore;

r = x/2 and the volume of the sphere is thus;

volume of the sphere = $\frac{4}{3} \pi \frac{x^3}{8}$ = $\frac{1}{6} \pi x^3$

For tank B

Volume of tank = x³

The volume of the spheres = $8 \times \frac{4}{3} \pi r^3$

However, the diameter of the spheres 2·D = x therefore;

r = x/4 and the volume of the sphere is thus;

volume of the spheres = $8 \times \frac{4}{3} \pi (\frac{x}{4})^3= \frac{x^3 \times \pi }{6}$

For tank C

Volume of tank = x³

The volume of the spheres = $64 \times \frac{4}{3} \pi r^3$

However, the diameter of the spheres 4·D = x therefore;

r = x/8 and the volume of the sphere is thus;

volume of the spheres = $64 \times \frac{4}{3} \pi (\frac{x}{8})^3= \frac{x^3 \times \pi }{6}$

Volume occupied by the spheres are equal therefore the three tanks contains the same volume of water

2) For the 4th tank, we have;

number of spheres on side of the tank, n is given thus;

n³ = 512

∴ n = ∛512 = 8

Hence we have;

Volume of tank = x³

The volume of the spheres = $512 \times \frac{4}{3} \pi r^3$

However, the diameter of the spheres 8·D = x therefore;

r = x/16 and the volume of the sphere is thus;

volume of the spheres = $512\times \frac{4}{3} \pi (\frac{x}{16})^3= \frac{x^3 \times \pi }{6}$

Amount of water remaining in the tank is given by the following expression;

Amount of water remaining in the tank = Volume of tank - volume of spheres

Amount of water remaining in the tank = $x^3 - \frac{x^3 \times \pi }{6} = \frac{x^3(6-\pi) }{6}$

$Amount \ of \ water \, remaining \, in \, the \ tank = \frac{x^3(6-\pi) }{6}$ .

5 0

3 years ago

Wesley earned $72 walking dogs for 6 hours. How many total hours will it take Wesley to earn $96 in all? Solve using unit rates.

MissTica

8 hours

72/6=12 $12 and hour 96/12=8 8 hours to earn $96

8 0

3 years ago

Instructions: Solve the following equation for the variable given.

frutty [35]

Answer:

x = -1

Step-by-step explanation:

1/4 (4x - 4) = -2(6x + 7)

1x - 1 = -12x - 14

13x = -13

x = -1

7 0

3 years ago

What is the greatest common factor you can use to divide the numerator and denominator of the fraction 28/32?

Anastaziya [24]

The greatest common factor is 4.

28/32 / 4 = 7/8

7 0

3 years ago

A rectangular yoga mat has a perimeter of 179 inches. The width of the mat is eight less than half the length. Find the width, i

lianna [129]

Answer:

The width is $24.5in$

Step-by-step explanation:

The perimeter of the rectangular yoga mat can be found using the formula;

$P=2l+2w$ .

$\Rightarrow 179=2l+2w...(1)$ .

It was given that the width of the mat is eight less than half the length.

$w=\frac{1}{2}l-8...(2)$

We put equation (2) into equation (1) to get;

$179=2l+2(\frac{1}{2}l-8)$ .

$\Rightarrow 179=2l+l-16$ .

$\Rightarrow 179+16=2l+l$ .

$\Rightarrow 3l=195$

Divide both sides by 3;

$l=65$

We put $l=65$ into equation 2 to get;

$w=\frac{1}{2}\times65-8$

$w=32.5-8$

$w=24.5in$

4 0

3 years ago